Exam 13: Inference About Comparing Two Populations

The F-distribution is the sampling distribution of the ratio of:

When comparing two population variances,we use the ratio rather than the difference .

In testing the difference between two population means for which the population variances are unknown and not assumed to be equal,two independent samples are drawn from the populations.Which of the following tests is appropriate?

Clinic Waiting Time In a random sample of 20 patients who visited a clinic at Medical Center 1,a researcher found that the variance of the waiting time (in minutes)was 128.0.In a random sample of 15 patients in the clinic of Medical Center 2,the researcher found the variance to be 178.8. -{Clinic Waiting Time Narrative} Estimate with 95% confidence the ratio of the two population variances and interpret.

Additives A food processor wants to compare two additives for their effects on retarding spoilage.Suppose 16 cuts of fresh meat are treated with additive A and 16 are treated with additive B,and the number of hours until spoilage begins is recorded for each of the 32 cuts of meat.The results are summarized in the table below -A calculus professor wanted to test whether the grades on calculus test were the same for upper and lower classmen.The professor took a random sample of size 12 from each group.For this situation,the professor should use a matched pairs t-test.

Given the information: the number of degrees of freedom that should be used in the pooled variance t-test is:

To estimate the ratio of the population variances you use the ____________________ of the ____________________ variances.

A political analyst in Hawaii surveys a random sample of registered Democrats and compares the results with those obtained from a random sample of registered Republicans.This would be an example of:

Engine Wear To compare the wearing of two types of automobile engines,1 and 2,an experimenter chose to "pair" the measurements,comparing the wear for the two types of engines on each of 7 automobiles,as shown below. -(Engine Wear Narrative} Determine whether these data are sufficient to infer at the 10% significance level that the two types of engines wear differently.

The expected value of the difference between two sample proportions is the difference between their corresponding population proportions.

The pooled variance estimator is the ____________________ average of the two sample variances.

The pooled proportion estimate is found by taking the proportion of successes from sample 1 plus the proportion of successes from sample 2.

A Marine boot camp instructor recorded the time in which each of 15 recruits completed an obstacle course both before and after basic training.To test whether any improvement occurred,the instructor would use a t-distribution with 15 degrees of freedom.

Motorcycle insurance appraisers examine motorcycles that have been involved in accidental collisions to assess the cost of repairs.An insurance executive is concerned that different appraisers produce significantly different assessments.In an experiment 10 motorcycles that have recently been involved in accidents were shown to two appraisers.Each assessed the estimated repair costs.These results are shown below.Can the executive conclude at the 5% significance level that the appraisers differ in their assessments?

A behaviorist has performed the following experiment.For each of 10 sets of identical twins who were born 30 years ago,he recorded their annual incomes,according to which twin was born first.The results (in $1,000s)are shown below.Can he infer at 5% significance level that there is a difference in income between the twins?

If the F-test statistic is large,that means the variance of Population 1 is ____________________ than/to the variance of Population 2.

The number of degrees of freedom associated with the t-test,when the data are gathered from a matched pairs experiment with 10 pairs,is:

The expected value of is .

The test for the equality of two population variances assumes that each of the two populations is normally distributed.

The F-distribution is symmetric.